a) b) Durbin-Watson test is a procedure which is utilised to check whether the errors ('s) on a time series data are positively autocorrelated or not. Briefly explain the three conditions used to determine the significance of the test. Clearly state the conclusion on each condition. What is meant by saying the least squares estimators are BLUE and under what conditions are the least squares estimators BLUE?
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- Percentages of public school students in fourth and eighth grades who were above the proficiency level were given for 8 western states 4th Grade Proficiency 8th Grade Proficiency Arizona 15 21 California 11 18 Hawaii 16 16 Montana 22 37 New Mexico 13 13 Oregon 21 32 Utah 23 26 Wyoming 19 25 Construct a scatterplot and comment on any interesting characteristics Find the least squares equation. If Nevada had a 4th grade proficiency of 14%, what would you expect the 8th grade proficiency to be?The accompanying table is used to make the preliminary computations forfinding the least squares line for the given pairs of x and y values.Based on a sample of n=25, the least-squares method was used to develop the prediction line Yi=8+3Xi. In addition, SYX=2.5, X=7, and ∑i=1nXi−X2=25. b. Construct a 90% prediction interval of an individual response for X=5. enter your response here≤YX=5≤enter your response here (Round to two decimal places as needed.)
- The least squares criterion is _____. a. min Σ(yi - ȳ)2 b. min (Σyi - ŷi)2 c. min Σ(xi - yi)2 d. min Σ(yi - ŷi)2A chi square test for homogeneity applies to: Select one: a. data from a single random sample where the sample is classified by values of three or more categorical variables. b. data from samples from two or more populations where each sample is classified by values of two categorical variables. c. data from samples from two or more populations where each sample is classified by values of a single categorical variable. d. data from a single random sample where the sample is classified by values of two categorical variables.Various doses of a poisonous substance were givento groups of 25 mice and the following results wereobserved: Dose (mg) Number of deathsx y4 16 38 610 812 1414 1616 20 (a) Find the equation of the least squares line fit tothese data.(b) Estimate the number of deaths in a group of 25 micethat receive a 7-milligram dose of this poison.
- Assume that the following tables are the results of Diagnostic tests. Why do you use the following test? What is the Null hypothesis? Interpret the results. White Test F-statistic 3.017495 Prob. F(14,29) 0.58 Obs*R-squared 26.08995 Prob. Chi-Square(14) 0.52 Why do you use the following test? What is the Null hypothesis? Interpret the results. Lagrange multiplier (LM) test F-statistic 22.78404 Prob. F(1,38) 0.0000 Obs*R-squared 16.49278 Prob. Chi-Square(1) 0.0000 Why do you use the following test? How can you interpret the results? Variance Inflation Factors Coefficient Uncentered Centered Variable Variance VIF VIF…Can you use these results and Theorem 12.2 (see image) to test the nullhypothesis that ? = 150 thousand miles against the alternative hypothesis ? < 150 thousand miles at the 0.01 level of significance for the following: the times to failure of a power train component in a certain car make and model are (in thousands of miles) 225, 459, 54, 180, 585, 558, 36, 342, 270, 378, 108, 396, 18, 252,135, 18, 162, 297, 171, and 27. Consider these data to be a random sample from an exponential (?) population.When a least squares line is fit to the 12 observations in the labor cost data, we obtain SSE =656, 214.3589. Calculate s2 and s (isnt n-k-1)?
- The following data show the advertising expenses(expressed as a percentage of total expenses) and thenet operating profits (expressed as a percentage of totalsales) in a random sample of six drugstores:Advertising Net operatingexpenses profits1.5 3.61.0 2.82.8 5.40.4 1.91.3 2.92.0 4.3 (a) Fit a least squares line that will enable us to predictnet operating profits in terms of advertising expenses.(b) Test the null hypothesis α = 0.8 against the alterna-tive hypothesis α > 0.8 at the 0.01 level of significance.A teacher is comparing the mena study time of his freshmen and senior students. He believes that his senior students spend more time studyin per week than his freshmen studnet and decides to perform a hypothesis test on his belief. a. Suppose the decision of the hypothesis test is to reject the null hypothesis. If, in realiry, treshmen study for a mean of 10 hours per week and seniors study for a mena of 15 hours per week, was an error made? if so, what type? b. Suppose the decision of the hypothesis test is to fail to reject the null hypothesis. if, in realiry, freshmen study for a mena of 15 hours per seek and seniors study for a mean of 15 hours per week, was an error made? is so, what type?Two varieties of lettuce were grown for 16 days in acontrolled environment. The following table shows the totaldry weight (in grams) of the leaves of nine plants of thevariety “Salad Bowl” and six plants of the variety “Bibb.” Compute the standard error of (Y1 - Y2) for these data.